Supposedly but that nice theory is not supported by the facts we have. For instance in BF1, PS4 drops down to ~30fps where it's CPU heavy in the 64 players mode, XB1 version drops to ~30fps in scenes where there is lots of fog (so alphas).Microsoft are a software company so it's no surprise they created a system more biased towards the cpu, with DDR3 lower bandwidth, lower latency ram vs DDR5 high bandwidth, higher latency ram, and Sony being a primarily hardware company chose to focus on the technical specs. In many ways the One is a more balanced system, and let's not forget that the edram is actually an advantage in games like BF1 which are heavy on alpha effects.
In BF1 in the modes where it's less CPU heavy (but still with lots of alphas) both versions run very similarly (with a very slight advantage for PS4 actually using the average fps), while PS4 still having the usual ~40% resolution advantage.
In Titanfall 2 a game with tons of alphas, the XB1 game drops down to 480p when the PS4 game drops down to 720p in those cases (both running at solid 60fps).
My take on this is that while esram may give an advantage in those cases, PS4 has twice the number of ROPS the XB1 has.